Final answer:
Io would lose approximately 0.159% of its mass over a period of 4.5 billion years at the constant rate of losing 1000 kg of sulfur dioxide per second to Jupiter's magnetosphere.
Step-by-step explanation:
The mass of Io is given as 8.93 x 1022 kg, and it loses about 1000 kilograms of sulfur dioxide per second to Jupiter's magnetosphere. Over a period of 4.5 billion years, which is 4.5 x 109 years, the total mass lost would be:
Total mass lost = Mass loss rate (kg/s) × number of seconds in 4.5 billion years
If we calculate the number of seconds in 4.5 billion years (4.5 x 109 years × 365.25 days/year × 24 hours/day × 3600 seconds/hour), we get approximately 1.42 x 1017 seconds. Multiplying this by the mass loss rate of 1000 kg/s gives us a total mass loss of 1.42 x 1020 kg.
To find the fraction of its mass that Io would lose, we divide the total mass lost by Io's initial mass:
Mass loss fraction = Total mass lost / Initial mass of Io = (1.42 x 1020 kg) / (8.93 x 1022 kg)
This fraction is approximately 0.00159. To express this as a percentage, we multiply by 100, which gives us 0.159% to two significant figures.